A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$7.50$, and bags of cookies cost $$2.50$, and sales equaled $$25.00$ in total. There were $2$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Solution: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${7.5x+2.5y = 25}$ ${y = x+2}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+2}$ for $y$ in the first equation. ${7.5x + 2.5}{(x+2)}{= 25}$ Simplify and solve for $x$ $ 7.5x+2.5x + 5 = 25 $ $ 10x+5 = 25 $ $ 10x = 20 $ $ x = \dfrac{20}{10} $ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $ {y = x+2}$ to find $y$ ${y = }{(2)}{ + 2}$ ${y = 4}$ You can also plug ${x = 2}$ into $ {7.5x+2.5y = 25}$ and get the same answer for $y$ ${7.5}{(2)}{ + 2.5y = 25}$ ${y = 4}$ $2$ bags of candy and $4$ bags of cookies were sold.